document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43222>Question 43222</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534494498/algebrahomeworkh>algebra and trigonometry with analytic geometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> find the point on the positive y-axis that is a distance 5 from the point P(3,4). I plotted it out to be B(0,8) But I'm not sure if this is right.  Thanks for looking it over. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #28247 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=28247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> CONSTRUCTIONAL METHOD:\r<BR>\n" );
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document.write( "First locate the point P(3,4) on a graph paper.<BR>\n" );
document.write( "Then draw a circle with centre at (3,4) and radius equal to 5 units.<BR>\n" );
document.write( "This circle intersects the y-axis at two points A and B.<BR>\n" );
document.write( "Find out the coordinates of these points from the graph.<BR>\n" );
document.write( "You shall find coordinates of A and B are (0,8) and (0,0) respectively.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C%0D%0Agrid%281%29%2C%0D%0Acircle%283%2C4%2C5%29%2C%0D%0Alocate%283%2C4%2CP%29%2C%0D%0Alocate%280.2%2C8%2CA%29%2C%0D%0Alocate%280.3%2C1%2CB%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Both points A and B lies on y-axis and are at a distance of 5 units from P but only A lies on the positive y-axis. So the required point is A and the coordinates are (0,8).\r<BR>\n" );
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document.write( "ALTERNATIVE METHOD:\r<BR>\n" );
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document.write( "The distance 'd' between two points (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is given<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D-y%5B2%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D-y%5B2%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ____________(1)\r<BR>\n" );
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document.write( "In this problem let the coordinates of A and B are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) respectively.<BR>\n" );
document.write( "Here, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ?<BR>\n" );
document.write( "[Note <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+0 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has to lie on y-axis] <BR>\n" );
document.write( "Putting these values in (1) we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+=+sqrt%28%283-0%29%5E2+%2B+%284-y%5B2%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"5+=+sqrt%28%283-0%29%5E2+%2B+%284-y%5B2%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Squaring both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2+=+3%5E2+%2B+%284-y%5B2%5D%29%5E2 ALIGN=MIDDLE  ALT=\"5%5E2+=+3%5E2+%2B+%284-y%5B2%5D%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2+-+3%5E2+=+%284-y%5B2%5D%29%5E2 ALIGN=MIDDLE  ALT=\"5%5E2+-+3%5E2+=+%284-y%5B2%5D%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+-+9+=+%284-y%5B2%5D%29%5E2 ALIGN=MIDDLE  ALT=\"25+-+9+=+%284-y%5B2%5D%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+%284-y%5B2%5D%29%5E2 ALIGN=MIDDLE  ALT=\"16+=+%284-y%5B2%5D%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2+-+%284-y%5B2%5D%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"4%5E2+-+%284-y%5B2%5D%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+%2B+%284-y%5B2%5D%29%29%284+-+%284-y%5B2%5D%29%29+=+0 ALIGN=MIDDLE  ALT=\"%284+%2B+%284-y%5B2%5D%29%29%284+-+%284-y%5B2%5D%29%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288-y%5B2%5D%29y%5B2%5D%29+=+0 ALIGN=MIDDLE  ALT=\"%288-y%5B2%5D%29y%5B2%5D%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+-+y%5B2%5D ALIGN=MIDDLE  ALT=\"8+-+y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0 i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8 or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.<BR>\n" );
document.write( "As the reqd. point must be on positive y-axis, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+8 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the only possibility.\r<BR>\n" );
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document.write( "Thus the coordinates of the point A which lie on positive y-axis and is at a distance of 5 units from (3,4) are (0,8). </SPAN>\n" );
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